Question

A rectangular piece is 20 meter long and 15 m wide . from its 4 corner , quadrants of radii 3.5 m have been cut. find the area of the remaining part

Answer 1

Answer:

$\large \frak{given }:$

• Length of rectangular piece l = 20m
• Breadth of rectangular piece b = 15m
• Radius of each quadrant r = 3.5m

$\sf \: Area \: of \: rectangular \: piece = (length × breadth) \\ \\ \sf \: Area \: of \: rectangular \: piece = 20 × 15 \\ \\ \sf \boxed{ \green{ \frak{ Area \: of \: rectangular \: piece = 300 m {}^{2} . }}}$

Area of quadrant each = 14(area of circle with radius 3.5m)

$\sf \: Area \: of \: quadrant \: each\: = \frac{1}{4} \pi {r}^{2} \\ \\ \sf \: \sf \: Area \: of \: quadrant \: each\: = \frac{1}{4} \times \frac{22}{7} \times {(3.5)}^{2} \\ \\ \sf \: \sf \: Area \: of \: quadrant \: each\: = \frac{1}{ \cancel4} \times \frac{ \cancel{22}}{7} \times 3.5 \times 3.5 \\ \\ \sf \: Area \: of \: quadrant \: each\: = \frac{5.5}{7} \times 3.5 \times 3.5 \\ \\ \sf \: Area \: of \: quadrant \: each\: = \frac{63.73}{7} \\ \\ \purple{\boxed{ \sf \frak{ Area \: of \: quadrant \: each\: = \frac{38.5}{4} \: {m}^{2} }}}$

$\bf \: Area \: of \: remaining \: part = [area \: of \: rectangular \: piece] \\ \bf– 4[area \: of \: each \: quadrant]$

$\sf \: Area \: of \: remaining \: part = 300 - \cancel 4 \times \frac{38.5}{ \cancel4} \\ \\ \sf \: Area \: of \: remaining \: part = 300 - 38.5 \\ \\ \boxed{\red{ \frak{Area \: of \: remaining \: part = 261.5 {m}^{2} }}}$

Hence, the remaining part of the area of the piece is 261.5 m²